just wondering: is it possible to show only groups at the “home”-page ?

Yes. You can add or remove whatever widgets you want to the bphome theme page.

Log into WPMU and go to “Appearance > Widgets”. On the right side of the screen, select which theme column you want to place a given widget, then click the “Add” button for that widget. Click on “Edit” for each widget to set certain parameters.

You can also remove any widget from any column by clicking a given widget’s “Edit” button and then clicking the “Remove” button. Just make sure to click the “Save Changes” button whenever making widget changes.

is it possible having “group-wide-activity” showing for each group also at the start-page ?

As far as I know, there currently is not a group-wide-activity widget. You can either make your own, or if you do not have coding experience, create a new thread in the “Requests & Feedback” forum asking for such a widget. Perhaps someone will make one!